1. Power of a Test

2. Remember: Type I error – Reject the H0 when you shouldn’t have.
Type II error - Fail to reject the Ho when you should have.

3. Fill in the chart with the type of error
Null is True
Null is False
Reject Null
Fail to Reject Null
By choosing a level of significance ( ) we determine the probability of committing a type I error.

4. Power of a Test: (1 – β)
It measures the sensitivity of the test to detect a real difference in parameters if one really exists.
Rejecting a False Ho.

5. To increase the power of a test we
Increase alpha
Use a larger sample size.
Null is True
Null is False
Reject Null
 Type I error (α)
Correct decision
(1-β)
Fail to Reject Null
 Correct decision
(1-α)
 Type II error (β)

6. Cigarette manufacturer claims that the mean nicotine content of its cigarettes is 1.5 mg. Researchers believe it’s more than this. Test a sample of 36 and find standard deviation is Use a 1% significance level. (Suppose it’s really 1.6)

7. A study claims that the mean weight of a book is 2. 4 pounds
A study claims that the mean weight of a book is 2.4 pounds. Researchers believe that it is more. Test a sample of 30 and st. dev. Is 0.5 pounds. Use 5% significance level. (What if it’s really 2.7 pounds?)

8. A study claims that the mean weight of a dog is 26. 8 pounds
A study claims that the mean weight of a dog is 26.8 pounds. Researchers believe that it’s less than this. Test a sample of 36 and st. dev. Is 2.2 pounds. Use 5% significance level. (What if it’s really 26 pounds?)

9. Homework
Worksheet